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Nanomanufacturing University of Michigan ME599-‐002 | Winter 2010
07: Intermolecular and surface forces
February 3, 2010
John Hart [email protected] hFp://www.umich.edu/~ajohnh
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Announcements § …
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Recap: thermal proper>es § Thermal energy in solids is carried by electrons and phonons
§ Fourier’s law (diffusive thermal transport) breaks down at small length scales and short Umes § Like electrical conductance, there is a quantum unit of thermal
conductance § QuanUzed thermal conductance has been measured at VERY low
temperatures in nanoscale structures, where the number of phonon modes is restricted
§ BallisUc phonon transport occurs in sub-‐micron length CNTs
§ Boundary scaFering of phonons reduces thermal conducUvity and governs interface conductance –this can be bad for contacts and good for thermoelectrics
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Course outline 0: IntroducUon to nanotechnology
1: ProperUes of nanostructures (“building blocks”)
2: InteracUons among nanostructures
3: Synthesis of nanostructures
4: Assembly of nanostructures and property scaling
5: Case studies and project presentaUons
Assignments: problem sets (4) exam (1), video assignment (1) project (1)
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~1 m
m~1
mm
©2010 | A.J. Hart | 7 Pugno, J. Phys. Cond. MaF 19:395001, 2007.
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Today’s agenda § Origin of intermolecular and surface forces § SummaUon of forces between solid bodies, based on pairwise interacUon potenUals
§ CalculaUon of van der Waals forces and adhesion forces for regular geometries
§ Methods of measuring surface forces § Adhesion in nature
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Today’s readings (ctools) Nominal: (on ctools) § Israelachvili, excerpts from Intermolecular and Surface Forces
§ Arzt et al., “From micro to nano contacts in biological aFachment devices”
Extras: (on ctools) § Bishop et al., “Nanoscale forces and their uses in self-‐assembly”
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Forces hold the universe together
Israelachvili.
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Classifica>on of intermolecular forces § Electrosta>c: Coulomb force between charges, and permanent dipole-‐dipole interacUons
§ Polariza>on: Dipole moments induced in atoms by electric fields of nearby charges, and by permanent dipoles
§ Quantum mechanical: give rise to chemical bonding
§ Short-‐range: <1 nm (close to contact) § Long-‐range: <100 nm
§ Exponent on the force law is always > 3 (i.e., 1/r>3), else interacUon energy would increase for long distances and large bodies
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Atomic, ionic, and molecular interac>ons
Israelachvili.
Quantum mechanical (bonding)
ElectrostaUc (charge-‐charge)
PolarizaUon (charge-‐dipole, dipole-‐dipole)
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Quantum mechanical (exclusion)
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Defini>on of van der Waals (VDW) forces
Israelachvili; hFp://goldbook.iupac.org/V06597.html.
The aFracUve or repulsive forces between molecular enUUes (or between groups within the same molecular enUty) other than those due to bond formaUon or to the electrostaUc interacUon of ions (or ionic groups) with one another or with neutral molecules. The term includes: dipole–dipole, dipole–induced dipole and London (instantaneous induced dipole–induced dipole) forces. The term is someUmes used loosely for the totality of nonspecific a\rac>ve or repulsive intermolecular forces.
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repulsive -‐ a\rac>ve
Lennard-‐Jones poten>al: neutral atoms or molecules
hFp://en.wikipedia.org/wiki/Lennard-‐Jones_potenUal Repulsive-‐aFracUve balance = colloid stability
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Summing pairwise interac>ons
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Sphere-‐plate (Langbein approxima>on)
( )( )( )( ) 5
2
54324)( −−−−−
−= nDnnnnRCDW ρπ
DRCDWn
6)( ,6
22 ρπ−==
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Derjaguin approxima>on
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Derjaguin approxima>on
( )
( )
)(2
2)(
11
112
2)(
21
21
21
21
21
21
2
21
DWRRRR
dZZfRRRRDF
xdxRR
dZ
RRxDzzDZ
ZxdxfDF
D
Z
DZ
⎟⎠
⎞⎜⎝
⎛+
=
⎟⎠
⎞⎜⎝
⎛+
≈
⎟⎠
⎞⎜⎝
⎛+=
⎟⎠
⎞⎜⎝
⎛++=++=
=
∫
∫
∞
∞=
=
π
π
π
§ F(Z), W(D) as derived for two planes § D << (R1,R2) § Applies to any force law
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Plane-‐plane versus sphere-‐sphere § Equilibrium at points where force is zero (local minima of interacUon energy)
Israelachvili.
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VDW energies for regular geometries
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Hamaker constant § How do we determine the pair potenUal constant (C) for calculaUons of total interacUon energy?
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Hamaker constants
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VDW-‐induced CNT deforma>on
Hertel et al., Physical Review B 58(20):13870, 1998.
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MWNT telescoping “bearings”
Cumings, Science 289:602, 2000.
§ RelaxaUon Ume = nanoseconds § VDW forces make this a constant-‐force spring
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Surface force apparatus (Israelachvili)
§ Adjustment using interchangeable and variable-‐sUffness springs
§ Use opUcal fringes to detect contact and measure separaUon
§ Calculate force knowing displacement and spring sUffness
§ SeparaUon controlled to 1 A
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Surface force apparatus (Israelachvili)
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(cap>ons for previous slides)
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Adhesion scaling in nature
Artl et al., PNAS 100(19):10603-‐10606, 2003.